Should Milner leave for Eastlands then it would be the second high-profile midfielder to leave the Midlands club for their rivals in two seasons, following Gareth Barry's £12m transfer to Manchester City last season.
City manager Roberto Mancini said this week that Milner remained on his shopping list, but that he did not want his club's spending power to be exploited by their competitors.
"When Manchester City want to buy a player, other clubs ask much more than is normal," stated the Italian.
"This is not good and it is not right. Until today, it is only City that are moving the market.
"We have bought three good players already. But now Inter Milan, for example, are asking a lot of money for striker Mario Balotelli, and we want to wait.
"We are interested in good players like Balotelli and Milner but we have time before the market closes in August. We have a lot of different choices."
Aston Villa centre-back Richard Dunne moved to the club from Manchester City last summer and has faith in O'Neill to replace Milner if the midfielder inevitably moves on.
"It's part of football," said Dunne. "He has had a great season so teams are going to be interested. If a club is going to offer enough money then players will move on.
"The manager has proven he can pick out a good player and usually, like James, he has bought them for a cheaper price than what he sells them for.
"The club will miss James who has been brilliant but we have to move on and the manager will build again, I suppose.
At Aston Villa he (Milner) will play every week, at Manchester City he may not
Aston Villa defender Richard Dunne
"James will know, because he is moving to a big club which wants to win the league, that he will be part of a squad. At Aston Villa he will play every week, at Manchester City he may not.
"But it's the opportunity where he thinks he can go and win the league.
"Man City is great club and he will enjoy himself there. Team-wise it's going to be difficult for everyone to get in the team."
Meanwhile, O'Neill's Villa have been linked with West Ham midfielder Scott Parker if Milner leaves.
West Ham co-owner David Sullivan said this week: "Aston Villa will not have enough money to tempt us to sell Scott Parker - he really is not for sale."
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